balance Quickstart (raking): Analyzing and adjusting the bias on a simulated toy dataset¶

The raking method is an advanced technique that extends post-stratification. It is well-suited for situations where we have marginal distributions of multiple covariates and we don't know the joint distribution. Raking works by applying post-stratification to the data based on the first covariate, using the resulting output weights as input for adjustment based on the second covariate, and so forth. Once all covariates have been utilized for adjustment, the process is repeated until a specified level of convergence is attained

One of the main advantages of raking is its ability to work with user-level data while also utilizing marginal distributions that lack user-level granularity. Another benefit is its capacity to closely fit these distributions, depending on the convergence achieved. This is in contrast to techniques such as inverse probability weighting (IPW) and covariate balancing propensity score (CBPS), which may only approximate the data and potentially fail to fit them even at marginal levels.

This notebook demonstrates how to use the raking method and showcases the high degree of fit it can provide.

Load the data¶

In [1]:
from balance import load_data

INFO (2023-06-28 06:05:04,101) [__init__/<module> (line 52)]: Using balance version 0.9.0
In [2]:
target_df, sample_df = load_data()

print("target_df: \n", target_df.head())
print("sample_df: \n", sample_df.head())

target_df: 
        id gender age_group     income  happiness
0  100000   Male       45+  10.183951  61.706333
1  100001   Male       45+   6.036858  79.123670
2  100002   Male     35-44   5.226629  44.206949
3  100003    NaN       45+   5.752147  83.985716
4  100004    NaN     25-34   4.837484  49.339713
sample_df: 
   id  gender age_group     income  happiness
0  0    Male     25-34   6.428659  26.043029
1  1  Female     18-24   9.940280  66.885485
2  2    Male     18-24   2.673623  37.091922
3  3     NaN     18-24  10.550308  49.394050
4  4     NaN     18-24   2.689994  72.304208
In [3]:
from balance import Sample

Raking can work with numerical variables since the variable is automatically bucketed. But for the simplicitiy of the discussion, we'll focus only on age and gender.

In [4]:
sample = Sample.from_frame(sample_df[['id', 'gender', 'age_group', 'happiness']], outcome_columns=["happiness"])
target = Sample.from_frame(target_df[['id', 'gender', 'age_group', 'happiness']], outcome_columns=["happiness"])
sample_with_target = sample.set_target(target)

WARNING (2023-06-28 06:05:04,343) [util/guess_id_column (line 111)]: Guessed id column name id for the data
WARNING (2023-06-28 06:05:04,353) [sample_class/from_frame (line 259)]: No weights passed. Adding a 'weight' column and setting all values to 1
WARNING (2023-06-28 06:05:04,365) [util/guess_id_column (line 111)]: Guessed id column name id for the data
WARNING (2023-06-28 06:05:04,383) [sample_class/from_frame (line 259)]: No weights passed. Adding a 'weight' column and setting all values to 1

Fit models using ipw and rake¶

Fit an ipw model:

In [5]:
adjusted_ipw = sample_with_target.adjust(method = "ipw")

INFO (2023-06-28 06:05:04,396) [ipw/ipw (line 428)]: Starting ipw function
INFO (2023-06-28 06:05:04,399) [adjustment/apply_transformations (line 257)]: Adding the variables: []
INFO (2023-06-28 06:05:04,400) [adjustment/apply_transformations (line 258)]: Transforming the variables: ['gender', 'age_group']
INFO (2023-06-28 06:05:04,410) [adjustment/apply_transformations (line 295)]: Final variables in output: ['gender', 'age_group']
INFO (2023-06-28 06:05:04,416) [ipw/ipw (line 462)]: Building model matrix
INFO (2023-06-28 06:05:04,492) [ipw/ipw (line 486)]: The formula used to build the model matrix: ['gender + age_group + _is_na_gender']
INFO (2023-06-28 06:05:04,493) [ipw/ipw (line 489)]: The number of columns in the model matrix: 7
INFO (2023-06-28 06:05:04,494) [ipw/ipw (line 490)]: The number of rows in the model matrix: 11000
INFO (2023-06-28 06:05:04,503) [ipw/ipw (line 521)]: Fitting logistic model
INFO (2023-06-28 06:05:06,212) [ipw/ipw (line 564)]: max_de: None
INFO (2023-06-28 06:05:06,216) [ipw/ipw (line 594)]: Chosen lambda for cv: [0.01729704]
INFO (2023-06-28 06:05:06,218) [ipw/ipw (line 602)]: Proportion null deviance explained [0.11516887]

Fit a raking model (on the user level data as input):

In [6]:
adjusted_rake = sample_with_target.adjust(method = "rake")

INFO (2023-06-28 06:05:06,235) [adjustment/apply_transformations (line 257)]: Adding the variables: []
INFO (2023-06-28 06:05:06,235) [adjustment/apply_transformations (line 258)]: Transforming the variables: ['gender', 'age_group']
INFO (2023-06-28 06:05:06,245) [adjustment/apply_transformations (line 295)]: Final variables in output: ['gender', 'age_group']
INFO (2023-06-28 06:05:06,257) [rake/rake (line 154)]: Final covariates and levels that will be used in raking: {'gender': ['Male', '__NaN__', 'Female'], 'age_group': ['35-44', '18-24', '45+', '25-34']}.

ipfn converged: convergence_rate below threshold

When comparing the results of ipw and rake, we can see that rake has a larger design effect, and that it provides a perfect fit. In contrast, ipw gives only a partial fit.

We can see it in the ASMD and also the bar plots.

In [7]:
print(adjusted_ipw.summary())

Covar ASMD reduction: 71.7%, design effect: 1.532
Covar ASMD (6 variables): 0.243 -> 0.069
Model performance: Model proportion deviance explained: 0.115
In [8]:
print(adjusted_rake.summary())

Covar ASMD reduction: 100.0%, design effect: 2.103
Covar ASMD (6 variables): 0.243 -> 0.000
In [9]:
adjusted_ipw.covars().plot()
In [10]:
adjusted_rake.covars().plot()

Using marginal distribution with rake¶

The benefit of rake is that we can define a target population from a marginal distribution, and fit towards it. The function to use for this purpose is prepare_marginal_dist_for_raking.

In order to demonstrate this point, let us assume we have another target population in mind, with different proportions. Since it is known, we can create a sample with that target population based on a dict of marginal distributions using the realize_dicts_of_proportions function.

In [11]:
from balance.weighting_methods.rake import prepare_marginal_dist_for_raking
# import pandas as pd
import numpy as np

a_dict_with_marginal_distributions = {"gender": {"Female": 0.1, "Male": 0.85, np.nan: 0.05}, "age_group": {"18-24": 0.25, "25-34": 0.25, "35-44": 0.25, "45+": 0.25}}

target_df_from_marginals = prepare_marginal_dist_for_raking(a_dict_with_marginal_distributions)
In [12]:
target_df_from_marginals
Out[12]:
gender age_group id
0 Female 18-24 0
1 Female 25-34 1
2 Male 35-44 2
3 Male 45+ 3
4 Male 18-24 4
5 Male 25-34 5
6 Male 35-44 6
7 Male 45+ 7
8 Male 18-24 8
9 Male 25-34 9
10 Male 35-44 10
11 Male 45+ 11
12 Male 18-24 12
13 Male 25-34 13
14 Male 35-44 14
15 Male 45+ 15
16 Male 18-24 16
17 Male 25-34 17
18 Male 35-44 18
19 NaN 45+ 19
In [13]:
target_df_from_marginals.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 20 entries, 0 to 19
Data columns (total 3 columns):
 #   Column     Non-Null Count  Dtype 
---  ------     --------------  ----- 
 0   gender     19 non-null     object
 1   age_group  20 non-null     object
 2   id         20 non-null     int64 
dtypes: int64(1), object(2)
memory usage: 608.0+ bytes

With the new target_df_from_marginals object ready, we can use it as a target. Notice that this makes sense ONLY for the raking method. This should NOT be used for any other method.

In [14]:
target_from_marginals = Sample.from_frame(target_df_from_marginals)
sample_with_target_2 = sample.set_target(target_from_marginals)

WARNING (2023-06-28 06:05:07,538) [util/guess_id_column (line 111)]: Guessed id column name id for the data
WARNING (2023-06-28 06:05:07,539) [sample_class/from_frame (line 188)]: Casting id column to string
WARNING (2023-06-28 06:05:07,549) [util/_warn_of_df_dtypes_change (line 1842)]: The dtypes of sample._df were changed from the original dtypes of the input df, here are the differences - 
WARNING (2023-06-28 06:05:07,550) [util/_warn_of_df_dtypes_change (line 1853)]: The (old) dtypes that changed for df (before the change):
WARNING (2023-06-28 06:05:07,551) [util/_warn_of_df_dtypes_change (line 1856)]: 
id    int64
dtype: object
WARNING (2023-06-28 06:05:07,552) [util/_warn_of_df_dtypes_change (line 1857)]: The (new) dtypes saved in df (after the change):
WARNING (2023-06-28 06:05:07,554) [util/_warn_of_df_dtypes_change (line 1858)]: 
id    object
dtype: object
WARNING (2023-06-28 06:05:07,554) [sample_class/from_frame (line 259)]: No weights passed. Adding a 'weight' column and setting all values to 1

And fit a raking model:

In [15]:
adjusted_rake_2 = sample_with_target_2.adjust(method = "rake")

INFO (2023-06-28 06:05:07,568) [adjustment/apply_transformations (line 257)]: Adding the variables: []
INFO (2023-06-28 06:05:07,569) [adjustment/apply_transformations (line 258)]: Transforming the variables: ['gender', 'age_group']
INFO (2023-06-28 06:05:07,573) [adjustment/apply_transformations (line 295)]: Final variables in output: ['gender', 'age_group']
INFO (2023-06-28 06:05:07,578) [rake/rake (line 154)]: Final covariates and levels that will be used in raking: {'gender': ['Male', '__NaN__', 'Female'], 'age_group': ['18-24', '35-44', '45+', '25-34']}.

ipfn converged: convergence_rate below threshold

As the following code shows, we get our data to have a perfect fit to the marginal distribution defined for age and gender.

In [16]:
print(adjusted_rake_2.summary())

Covar ASMD reduction: 100.0%, design effect: 2.176
Covar ASMD (6 variables): 0.341 -> 0.000
In [17]:
adjusted_rake_2.covars().plot()
In [ ]: